Understanding Compound Paths in Adobe Illustrator

In response to a question from Von Glitschka, here is a detailed (and technical) explanation of Compound Paths, Compound Shapes, Pathfinder, and all that jazz in Adobe Illustrator.
Original question from Von is posted here: • Compound Path Problems...
Follow up information from Monika Gause is posted here:
vimeo.com/1164...